In this study, the free vibration of three layered sandwich cylinders is considered. The flexural vibration of the main elastic
cylinder is damped using viscoelastic core which is discontinuously constrained by a number of elastic segments around
the circumference. The core layer is assumed to be linear viscoelastic with complex elastic moduli. For development of the
analytical procedure, the governing equation for the free vibration of a damped system is formulated. As a result a sixth order
differential equation for the motion is derived six boundary conditions in terms of flexural displacement are satisfied for
fixed-free and free-free discontinuously damped sandwich cylinders. The determinant of the coefficient matrix is then equated
to zero and roots are computed using the iteration method. The effects of the viscoelastic core with complex shear modulus
and the elastic modulus constrained layer on the dimensionless frequencies and the loss factors are computed for different
shear parameter, geometric parameter, and the core loss factor.
1 Ross, D., U. Ungar and U. Kerwin, “Damping of plate flexural vibrations by means of viscoelastic laminae,” Structural
Damping (ASME), section (3), 1959.
2 Mead, D.J. and S. Markus, “The Forced vibration of a three-layered, damped sandwich beam with Arbitrary Boundary
Conditions,” Journal of Sound and Vibration, vol. 10, 2, pp. 163-175, 1969.
3 Hotchkiss, A., “Constrained layer damping applied to a cantilever tube,” ISVR Technical Report, No. 64, University of
4 Hamidzadeh, H.R. and D. Chandler, “Circumferential vibrations of three layered sandwich cylinders,” The Proceedings
of the Thirteenth Biennial ASME Conference on Mechanical Vibrations and Noise, DE 36: 233- 237, 1991.
5 Hamidzadeh, H.R. and N.N. Sawaya, “Free vibration of thick multi-layer cylinders,” Journal of Shock and Vibrations, 2
(5), 393-401, 1995
6 Hamidzadeh, H.R., “The effect of viscoelastic core thickness on modal loss factors of a thick three-layer cylinder,”
Journal of Multi-body Dynamics, vol. 223, 1, pp. 1-8, 2009.
7 Nehru, E.S., “Axisymmetric Vibration of Piezo-Lemv Composite Hollow Multilayer Cylinder,” International Journal of
Mathematics and Mathematical Sciences, vol. 2012, Article ID 406364, 12 pages, 2012. doi:10.1155/2012/406364.
8 Li, S.R., X.H. Fu and R.C. Batra, “Free vibration of three-layer circular cylindrical shells with functionally graded
middle layer,” Mechanics Research Communications, vol. 37, 6, pp. 577-580, 2010.
9 Mohammadi, F. and R. Sedaghati, “Linear and nonlinear vibration analysis of sandwich cylindrical shell with constrained
viscoelastic core layer,” International Journal of Mechanical Sciences, vol. 54, 1, pp. 156-171, 2012